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Some properties of a subclass of uniformly convex functions with negative coefficients. (English) Zbl 1159.30307

Summary: The aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close-to-convexity, starlikeness and convexity for functions belonging to the subclass \(TS_\lambda(n,\alpha,\beta)\) of uniformly convex functions with negative coefficients. We also derive many results for the modified Hadamard products of functions belonging to the class \(TS_\lambda(n,\alpha,\beta)\), and obtain several interesting distortion theorems for certain fractional operators of functions in this class. Finally, we consider integral operators associated with functions in this class.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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